### Advanced Mathematics II (ID) (Summer Semester 2012)

- Lecturer: Prof. Dr. Maria Axenovich, Dipl.-Math. Marc Mitschele
- Classes: Lecture (3102001), Problem class (3102002)
- Weekly hours: 4+2

This class is mandatory for students enrolled in the International program in Mechanical Engineering at the Carl-Benz School of Engineering.

**This is the homepage for the Advanced Mathematics II class in the summer semester 2012.**

# +++ Examination in AM1, AM2 and AM3 +++

You can find detailed information to the exams on the following sites:

Exam in Advanced Mathematics 1

Exam in Advanced Mathematics 2

Exam in Advanced Mathematics 3

Schedule | ||
---|---|---|

Lecture: | Monday 9:45-11:15 | ID SR Raum 202 |

Wednesday 8:00-9:30 | ID SR Raum 203 | |

Problem class: | Thursday 11:30-13:00 | ID SR Raum 202 |

Lecturers | ||
---|---|---|

Lecturer | Prof. Dr. Maria Axenovich | |

Office hours: Fr. 10:00-11:00 | ||

Room 1.043 Kollegiengebäude Mathematik (20.30) | ||

Email: maria.aksenovich@kit.edu | ||

Problem classes | Dipl.-Math. Marc Mitschele | |

Office hours: | ||

Room 3A-11.2 Allianz-Gebäude (05.20) | ||

Email: marc.mitschele@kit.edu |

# Content

The topics of the lecture are:

- vector spaces
- differential equations
- the Laplace transformation
- vector valued functions of several variables

# Tutorial

We offer a tutorial, where a tutor (Weixuan Zhang, zhangweixuanpeter@googlemail.com , a senior student) discusses problems/problem sheets with you. This tutor will also correct your homework.

During the semester the tutorial will take place each Friday from 2 to 3:30 pm, in the seminar room ID SE 203.

Please note that the tutorials start on April 20th, 2012.

# Problem Sheets

Every week, a new worksheet with 5 problems will be handed out. On each problem you can get up to 10 points. Your solutions must be handed in the next week. Please hand in your homework into the AM2-box near seminar room Z1, building 01.85 (Fritz-Erler-Str. 1-3) or give it to your tutor.

During the semester you will find more information on problems here. Additionally we offer some practice tests.

The problem sheets will be handed out in class. You can also download them as pdf-files below.

Sheet | Solutions | Test | Date | Due | Topics |

Sheet 1 | loesungen1.pdf@hm2mach2012s@iag1|Solution 1 | test202@iag1|T 2 | 18.04.12 | 25.04.12 | Vector spaces, linear combinations, intersections |

Sheet 2 | loesungen2.pdf@hm2mach2012s@iag1|Solution 2 | test202@iag1|T 2 | 25.04.12 | 02.05.12 | Linear dep./indep., span, dimension, lines and planes |

Sheet 3 | loesungen3.pdf@hm2mach2012s@iag1|Solution 3 | test203@iag1|T 3 | 02.05.12 | 09.05.12 | Matrices, linear mappings, rotation, reflection |

Sheet 4 | loesungen4.pdf@hm2mach2012s@iag1|Solution 4 | test203@iag1|T 3 , test204@iag1|T 4 | 09.05.12 | 16.05.12 | Linear systems, regular and singular matrices, determinant |

Sheet 5 | loesungen5.pdf@hm2mach2012s@iag1|Solution 5 | test204@iag1|T 4 , test205@iag1|T 5 | 16.05.12 | 23.05.12 | Determinants, eigenvalues, eigenvectors |

Sheet 6 | loesungen6.pdf@hm2mach2012s@iag1|Solution 6 | test206@iag1|T 6 | 23.05.12 | 30.05.12 | Differential equations, constant coefficients, Euler type, reduction of the order |

Sheet 7 | loesungen7.pdf@hm2mach2012s@iag1|Solution 7 | test207@iag1|T 7 | 30.05.12 | 06.06.12 | Systems of differential equations, fundamental system, Wronskian, initial value problems |

Sheet 8 | loesungen8.pdf@hm2mach2012s@iag1|Solution 8 | test208@iag1|T 8 | 06.06.12 | 13.06.12 | Initial value problems, undetermined coefficients |

Sheet 9 | loesungen9.pdf@hm2mach2012s@iag1|Solution 9 | test208@iag1|T 8,test209@iag1|T 9 | 13.06.12 | 20.06.12 | Variation of parameters, reduction of the order, power series ansatz |

Sheet 10 | loesungen10.pdf@hm2mach2012s@iag1|Solution 10 | test209@iag1|T 9 | 20.06.12 | 27.06.12 | Generalized power series, Euler's method, parameter integrals |

Sheet 11 | loesungen11.pdf@hm2mach2012s@iag1|Solution 11 | test210@iag1|T 10,test211@iag1|T 11 | 27.06.12 | 04.07.12 | Partial fraction decomposition, Laplace transform, Heaviside function, initial value problems |

Sheet 12 | loesungen12.pdf@hm2mach2012s@iag1|Solution 12 | test211@iag1|T 11 | 04.07.12 | 11.07.12 | Laplace transform and initial value problems, convolution, distributions |

Sheet 13 | loesungen13.pdf@hm2mach2012s@iag1|Solution 13 | test212@iag1|T 12 | 11.07.12 | 18.07.12 | Vector valued functions of several variables, norms, differentiability, linearisation, chain rule |

# The testat

If you successfully work on the home work and the in class quizzes, a testat will be given to you at the end of the semester, which is required for registration for the exam.

Please note: The AM II exam is part of the Orientierungsprüfung, which you must complete by the end of the third semester.

For the testat, you have to satisfy the following criteria:

- obtain at least 135 points on worksheets 1 to 11. This is approximately 25% of all the total points obtainable (each worksheet is worth 50 points)
- have at least 5 points from at least 8 of those worksheets.

- Each week there will be a short in class quiz, which is worth 5 points maximum. You need to get at least 30 points on 12 quizzes and obtain at least 1 point on each of at least 10 quizzes.

# Additional material

- Maple Worksheets for the AM lectures

# Examination

Please note: The AM II exam is part of the Orientierungsprüfung, which you must complete by the end of the third semester.

The examinations in Advanced Mathematics II will take place on August 4, 2012, 9.00-11.00 am. During the exam the use of the following materials is allowed:

- the AM I and AM II lecture notes including any handwritten notes in your copy,
- a printed book of formulae,
- one mathematical text book.

It is not allowed to use any electronical devices (calculator, etc.) and collections of old exams or other material.

# References

Besides the lecture notes, we recommend the following text books

- T. Arens, F. Hettlich, Ch. Karpfinger, U. Kockelkorn, K. Lichtenegger, H. Stachel:
*Mathematik.*Spektrum Akademischer Verlag, Heidelberg (in German). - K. Burg, H. Haf, F. Wille:
*Höhere Mathematik für Ingenieure.*Volumes I-III. Teubner Verlag, Stuttgart (in German).

- C.H. Edwards, D.E. Penney:
*Elementary Differential Equations with Boundary Value Problems.*Prentice Hall, 6th ed. - P.R. Halmos:
*Finite-Dimensional Vector Spaces.*Princeton, N.J., 2nd ed. - J. Hefferon:
*Linear Algebra.*Free textbook, can be downloaded from the author's webpage: here. - G. James:
*Advanced Modern Engineering Mathematics.*(4th edition) Pearson, 2011. - D.C. Lay:
*Linear Algebra and Its Applications.*Addison Wesley, 4th ed. - J. Stewart:
*Calculus, Early Transcendentals.*Brooks/Cole Publishing Company.